CDS Pricing with Counterparty Risk

Abstract

This thesis focuses on the impact of counterparty-risk in CDS (Credit Default Swap) pricing. The exponential growth of the Credit Derivatives Market in the last decade demands an upsurge in the fair valuation of various credit derivatives such as the Credit Default Swap (CDS), the Collateralized Debt Obligation (CDO). Financial institutions suffered great losses from Credit Derivatives in the sub-prime mortgage market during the credit crunch period. Counterparty risk in CDS contracts has been intensively studied with a focus on losses for protection buyers due to joint defaults of counterparty and reference entity. Using a contagion framework introduced by Jarrow and Yu (2001)[48], we calculate the swap premium rate based on the change of measure technique, and further extend both the two-firm and three-firm model (with defaultable protection buyer) with continuous premium payment. The results show more explanatory power than the discrete case. We improve the continuous contagion model by relaxing the constant intensity rate assumption and found close results without loss of generality. Empirically this thesis studies the behaviour of the historical credit spread of 55 sample corporates/ financial institutions, a Cox–Ingersoll–Ross model is applied to calibrate spread parameters. A proxy for counterparty spread is introduced as the difference between the spread over benchmark rate and spread over swap rate for 5 year maturity CDS. We then investigate counterparty risk during the crisis and study the shape of term structure for the counterparty spread, where Rebonato’s framework is deployed to model the dynamics of the term structure using a regime-switching framework.